Question

Solve each triangle.

$a=2,b=2,c=2$

Short answer

The required triangle is

$$\begin{gathered} A=60° \\ B=60° \\ C=60° \end{gathered}$$

Step-by-step solution

Given information

$a=2,b=2,c=2$

To find the angles A,B,C

Calculation

$$\begin{gathered} ForA: \\ \cos \left(A\right)=\frac{b^2+c^2-a^2}{2bc} \\ =\frac{2^2+2^2-2^2}{2\times 2\times 2} \\ =0.5 \\ A={\cos }^{-1}\left(0.5\right) \\ =60° \end{gathered}$$

$$\begin{gathered} ForB: \\ \cos \left(B\right)=\frac{a^2+c^2-b^2}{2ac} \\ =\frac{2^2+2^2-2^2}{2\times 2\times 2} \\ =0.5 \\ B={\cos }^{-1}\left(0.5\right) \\ =60° \end{gathered}$$

Since we know A and B,

$$\begin{gathered} C=180°-A-B \\ =180°-60°-60° \\ =60° \end{gathered}$$